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Q.
If the $n^{\text {th }}$ term of a G.P. $2,8,32, \ldots .$. is $131072$ , then the value of $n$ is
Sequences and Series
Solution:
$\because 131072$ be the $n^{\text {th }}$ term of given G.P.
Therefore, $ 131072=a_n=2(4)^{n-1} (\because a=2$ and $r=4)$
$\Rightarrow 65536 =(4)^{n-1}$
$\Rightarrow 4^8 =4^{n-1}$
$\Rightarrow 8 =n-1 $
$\Rightarrow n =9$
Hence, $131072$ is the $9^{\text {th }}$ term of the G.P. .